I just take the near side of the tire off, feel the inside surface of the tire until I find what caused the puncture, remove it, (you can usually flip the side of the tire up enough to see into it) pull that little section of tube out, find the hole (it can be so small you can barely see it!) patch it, and pop it back in. The most important thing is finding the sharp thing that punctured the tire, without stabbing yourself with it.

Nanci